Technical Report: Vibration and its Sensors 4

Torsional vibration occurs with rotation. However, torsional vibration can be broadly categorized into two types: in a rotating system where the drive unit and load unit are directly connected, it is caused by rotational fluctuations in the rotating unit; and in a multi-axis system combining gears, belts, chains, etc., it is caused not only by rotational fluctuations but also by transmission errors due to machining inaccuracies and deformation of the transmission unit. In actual equipment, these rotational fluctuations, torsional vibrations, and transmission errors are typically intertwined in a complex manner.

In systems where rotational fluctuations, torsional vibrations, and transmission errors occur, various adverse effects can arise. For example;

1. Increase in vibration and noise

2. Deterioration of positioning accuracy

3. Deterioration of feed accuracy

4. Fatigue failure

Therefore, in systems including rotating and transmission parts, it is important to measure rotational fluctuations, torsional vibrations, and transmission errors and analyze their causal relationships.

This represents the increase or decrease (variation) in rotational angular velocity relative to the average angular velocity at a single point on the axis of rotation. The measurement is performed using a high-resolution rotary encoder, and the output obtained is converted to F/V at high speed for each pulse to determine the rotational variation per revolution.

This refers to the relative angular displacement variation between two points on a rotating axis. Generally, electromagnetic rotation sensors are used in pairs to detect the torsion of the drive and load axes as a phase difference. The obtained phase difference is then converted using high-speed F/V conversion and calculated using frequency calculation.

This refers to the lag or lead in the rotation angle before and after the transmission device in multi-axis rotating machinery. The measurement is basically the same as for torsional vibration detection: the phase difference before and after the transmission device is detected, the transmission error per pitch is determined, and the value is calculated by frequency calculation.

Finally, here are the formulas for the conversion between acceleration, velocity, and displacement.

From the above equation, if frequency f and one of the following physical quantities—displacement D, velocity V, and acceleration G—can be measured, the other two can be calculated.